I've read up on tennis a fair deal, and this is one issue that I've yet to see be addressed. When serving, how should a player modify their serve when they shift from serving from the right of their opponent to the left, and vice versa (since when serving from the right, the serve should travel left, and when serving from the left, it should travel right).

Well, from experience, when you serve to your left (supposing you're right-handed), you just do a more natural movement, as the serve movement itself is "closed", that means, the follow-through goes in that direction. When you serve to your right, you should do a more open movement, guiding the racket's head in that direction, but you should finish it just like the other movement. I guess it's hard to explain. Try watching a good player serving/coach.